Finite-time extended state observer and fractional-order sliding mode controller for impulsive hybrid port-Hamiltonian systems with input delay and actuators saturation: Application to ball-juggler robots

This paper addresses the robust control problem of mechanical systems with hybrid dynamics in port-Hamiltonian form. It is assumed that only the position states are measurable, and time-delay and saturation constraint affect the control signal. An extended state observer is designed after a coordinate transformation. The effect of the time delay in the control signal is neutralized by applying Pade ́ approximant and augmenting the system states. An assistant system with faster convergence is developed to handle actuators saturation. Fractional-order sliding mode controller acts as a centralized controller and compensates for the undesired effects of unknown external disturbance and parameter uncertainties using the observer estimation results. Stability analysis shows that the closed-loop system states, such as the observer tracking error, and the position/velocity tracking errors, are finite-time stable. Simulation studies on a two ball-playing juggler robot with three degrees of freedom validate the theoretical results’ effectiveness

On the control of paraplegic standing using functional electrical stimulation

This thesis is concerned with the restoration of upright standing after spinal cord injury (SCI) by the means of Functional Electrical Stimulation. In particular, the work presented in this thesis is concerned with unsupported standing, i.e. standing without any support by the arms for stabilisation. Firstly, the experimental apparatus and feedback control approach is described. Secondly, the experimental work is divided into three parts. The motivation, experimental setup and procedure as well as results and conclusions are given for each of them. The feasibility of the investigated approach was usually tested on a neurologically intact subject. The results were subsequently confirmed with a paraplegic subject. First the feasibility and fundamental limitations of unsupported standing were investigated. Assuming the subject as a single-link inverted pendulum, an improved fully dynamic control approach was employed in the first step, confirming existing results. Here, the voluntary influence by the central nervous system was minimised. However, it is naturally desirable to take advantage of the residual sensory-motor abilities of the paraplegic subject to ease the task of stabilising the body. Ankle stiffness control has been proposed in the literature to accomplish this task. Hitherto, ankle stiffness was provided by artificial actuators. In the second part we investigated the feasibility and limitations of ankle stiffness control by means of FES. The same single-link approach was employed as above. Ankle stiffness control by FES was used in the third part to enable paraplegic standing. Here, the subject was required to participate actively in the task of stable standing and, while doing so, behaving like a double-link inverted pendulum. It could be shown that FES-controlled ankle stiffness contributed crucially to the subject's ability to stand. The thesis concludes with propositions for future work

Finite-Time H

This paper investigates the finite-time control problem for discrete-time Markov jump systems subject to saturating actuators. A finite-state Markovian process is given to govern the transition of the jumping parameters. The finite-time H∞ controller via state feedback is designed to guarantee that the resulting system is mean-square locally asymptotically finite-time stabilizable. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic control performance of discrete-time Markov jump systems are derived in the form of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach